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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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On the $W$-action on $B$-sheets in positive characteristic
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by Friedrich Knop and Guido Pezzini PDF
Represent. Theory 19 (2015), 9-23 Request permission

Abstract:

Let $G$ be a connected reductive group defined over an algebraically closed base field of characteristic $p\ge 0$, let $B\subseteq G$ be a Borel subgroup, and let $X$ be a $G$-variety. We denote the (finite) set of closed $B$-invariant irreducible subvarieties of $X$ that are of maximal complexity by $\mathfrak {B}_{0}(X)$. The first named author has shown that for $p=0$ there is a natural action of the Weyl group $W$ on $\mathfrak {B}_{0}(X)$ and conjectured that the same construction yields a $W$-action whenever $p\ne 2$. In the present paper, we prove this conjecture.
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Additional Information
  • Friedrich Knop
  • Affiliation: Department Mathematik, FAU Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
  • MR Author ID: 103390
  • ORCID: 0000-0002-4908-4060
  • Guido Pezzini
  • Affiliation: Department Mathematik, FAU Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
  • MR Author ID: 772887
  • Received by editor(s): September 2, 2013
  • Received by editor(s) in revised form: November 10, 2014, and February 3, 2015
  • Published electronically: March 6, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Represent. Theory 19 (2015), 9-23
  • MSC (2010): Primary 20G15, 14M17, 14L30, 20G05
  • DOI: https://doi.org/10.1090/S1088-4165-2015-00464-9
  • MathSciNet review: 3318502